10677 ÷ 4 = 2669 R1
Let's divide 10677 by 4.

Step 1:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 4

Step 2:
4 goes into 10 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 8 from 10 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 4

Step 3:
4 goes into 26 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 26
Subtract 24 from 26 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 4

Step 4:
4 goes into 27 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 266
Subtract 24 from 27 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 4

Step 5:
4 goes into 37 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 2669
Subtract 36 from 37 to get 1.

The final result is 2669 with a remainder of 1.